Interview Questions on Test Divisibility

x

Option: B

Explanation

sum of digits at odd places - sum of digits at even places should be 0 or divisible by 11

(6 + 5 + 2 + 9) - (# + 1 + 7) = (14 - #)

The least number which is subtracted with 14(i.e. instead of #) so that the number is divisible by 11 is 3

so 14 - 3 = 11 is divisible by 11

x

Option: A

Explanation

split 45 into co-primes

i.e. 45 = 5 x 9, 5 & 9 are co-primes

the number should be divisible by both 5 & 9

unit digit must be 0 or 5(286020),so the number is divisible by 5

(2 + 8 + 6 + 0 + 2 + 0) = 18, which is divisible by 9

286020 is divisible by 45

x

Option: A

Explanation

split 99 into co-primes

i.e. 99 = 11x9, 11 & 9 are co-primes

the number should be divisible by both 11 & 9

(5 + 3 + 1) - (4 + 4 + 1) = 0, which is divisible by 11

(1 + 1 + 4 + 3 + 4 + 5) = 18, which is divisible by 9

114345 is divisible by 99

x

Option: D

Explanation

split 72 into co-primes

i.e. 72 = 8 x 9, 8 & 9 are co-primes

the number is divisible by both 8 & 9

(4 + 6 + 4 + 9 + 0 + #) = 23 + #, least number of # is 4, 27 divisible by 9

last three digit now becomes 904 which is divisible by 8

so that value of # = 4

x

Option: C

Explanation

80 = 10 x 8

the number is divisible by both 8 & 9

as the number is divisible by 10, last digit must be 0

i.e. Y = 0

last three digits now becomes 3X0 which is divisible by 8, when X = 2

value of X = 2

X + Y = 2 + 0 = 2

Value of X + Y = 2